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Research Papers

# Control of Circumferential Wall Stress and Luminal Shear Stress Within Intact Vascular Segments Perfused Ex Vivo

[+] Author and Article Information
Mohammed S. El-Kurdi

Department of Surgery, Department of Bioengineering, McGowan Institute for Regenerative Medicine, The Center for Vascular Remodeling and Regeneration, University of Pittsburgh, Pittsburgh, PA 15219

Jeffrey S. Vipperman

Department of Mechanical Engineering and Material Science, Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15219

David A. Vorp1

Department of Surgery, Department of Bioengineering, McGowan Institute for Regenerative Medicine, The Center for Vascular Remodeling and Regeneration, University of Pittsburgh, Pittsburgh, PA 15219vorpda@upmc.edu

1

Corresponding author.

J Biomech Eng 130(5), 051003 (Jul 10, 2008) (7 pages) doi:10.1115/1.2948419 History: Received July 24, 2007; Revised April 02, 2008; Published July 10, 2008

## Abstract

Proportional, integral, and derivative (PID) controllers have proven to be robust in controlling many applications, and remain the most widely used control system architecture. The purpose of this work was to use this architecture for designing and tuning two PID controllers. The first was used to control the physiologic arterial circumferential wall stress (CWS) and the second to control the physiologic arterial shear stress (SS) imposed on intact vascular segments that were implanted into an ex vivo vascular perfusion system (EVPS). In order to most accurately control the stresses imposed onto vascular segments perfused ex vivo, analytical models were derived to calculate the CWS and SS. The mid-vein-wall CWS was calculated using the classical Lamé solution for thick-walled cylinders in combination with the intraluminal pressure and outer diameter measurements. Similarly, the SS was calculated using the Hagen–Poiseuille equation in combination with the flow rate and outer diameter measurements. Performance of each controller was assessed by calculating the root mean square of the error (RMSE) between the desired and measured process variables. The performance experiments were repeated ten times $(N=10)$ and an average RMSE was reported for each controller. RMSE standard deviations were calculated to demonstrate the reproducibility of the results. Sterile methods were utilized for making blood gas and temperature measurements in order to maintain physiologic levels within the EVPS. Physiologic blood gases (pH, $pO2$, and $pCO2$) and temperature within the EVPS were very stable and controlled manually. Blood gas and temperature levels were recorded hourly for several $(N=9)$$24h$ perfusion experiments. RMSE values for CWS control $(0.427±0.027KPa)$ indicated that the system was able to generate a physiologic CWS wave form within 0.5% error of the peak desired CWS over each cardiac cycle. RMSE values for SS control $(0.005±0.0007dynes∕cm2)$ indicated that the system was able to generate a physiologic SS wave form within 0.3% error of the peak desired SS over each cardiac cycle. Physiologic pH, $pO2$, $pCO2$, and temperature levels were precisely maintained within the EVPS. The built-in capabilities and overall performance of the EVPS described in this study provide us with a novel tool for measuring molecular responses of intact vascular segments exposed to precisely simulated arterial biomechanical conditions.

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## Figures

Figure 1

Schematic of one loop of the paired perfusion system. Note that there are two separate closed loops: the perfusate loop and the adventitial bathing loop. The components comprising both loops are (1) perfusate reservoir, (2) metal heat exchanger tubes inside water baths, (3) roller pumps, (4) pulse dampener, (5) one-way valve, (6) piston-cylinder device, (7) vessel cannulae, (8) pressure transducers, (9) tissue housing chamber, (10) inline thermistors, (11) self-sealing media sampling ports, (12) ultrasonic flow transducer, (13) needle-valve flow resistor, and (14) overflow recirculation line.

Figure 2

(a) Arterial pressure wave form that was used to calculate the CWS profile (b). (c) Arterial flow rate wave form that was used to calculate the SS profile (d).

Figure 3

Schematic showing the overall architecture of the PID controllers with implemented safety precautions.

Figure 4

Several representative wave forms from the controller performance experiments. The left panel shows the measured and set CWS wave forms, and the right panel shows the measured and set SS wave forms.

Figure 5

Blood gas and temperature control measurements made within our EVPS for several (N=9)24h perfusion experiments. The panels on the left are perfusate measurements and the panels on the right are bathing media measurements. Please note that each set of measurements is an average of the measurements made from the test and control loops of the paired system.

Figure 6

Leak simulation experiment results. As desired, in the event of a leak, the piston stops and the roller pump slows to supply a minimal flow rate of approximately 20ml∕min.

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